Suppose all individuals have a utility function of U = √C, where C is the amount of consumption a person has in any given period. There are two types of people: those at high risk, with a 4% chance of accident, and those at low risk, with a 2% chance of accident. Half of individuals are high risk, and half are low risk. The income of all individuals is $40,000 per year, and a catastrophic accident costs $30,000 in the year of the accident.

a. Calculate the actuarially fair insurance premium for each type of person, assuming the insurance company can identify who is high risk and who is low risk.

b. How much will a high-risk individual be willing to pay for insurance? A low-risk individual?

c. Suppose a law passes requiring community rating, and all insurance contracts must be priced the same. Insurers are forward-looking, and know about the composition and preferences of people in the insurance market, but are forbidden from using that information to set prices. What would be the price for insurance, and who would purchase insurance?

d. The legislature is considering two possible additional regulations on top of community rating: a mandate, and subsidies. The mandate would charge anyone failing to purchase insurance $100. The subsidies would give anyone purchasing insurance $100 to offset the price of the insurance.

Under this scheme, what would the price be for insurance and who would purchase it?

e. How do the results above relate to Massachusetts’ and the ACA health care reform strategies?